The existence of magnetic dipolar nanoparticle chains at zero field has been predicted theoretically for decades, but these structures are rarely observed experimentally. A prerequisite is a permanent magnetic moment on the particles forming the chain. Here we report on the observation of magnetic dipolar chains of spherical iron oxide nano particles with a diameter of 12.8 nm. The nanoparticles are embedded in an ultrathin polymer film. Due to the high viscosity of the polymer matrix, the dominating aggregation mechanism is driven by dipolar interactions. Smaller iron oxide nanoparticles (8 nm) show no permanent magnetic moment and do not form chains but compact aggregates. Mixed monolayers of iron oxide nanoparticles and polymer at the air-water interface are characterized by Langmuir isotherms and in situ X-ray reflectometry (XRR). The combination of the particles with a polymer leads to a stable polymer nanocomposite film at the air-water interface. XRR experiments show that nanoparticles are immersed in a thin polymer matrix of 2 nm. Using atomic force microscopy (AFM) on Langmuir-Blodgett films, we measure the lateral distribution of particles in the film. An analysis of single structures within transferred films results in fractal dimensions that are in excellent agreement with 2D simulations.